Properties

Label 3.542.1084.17.15
Class number $17$
Dimension $3$
Determinant $542$
Level $1084$

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Lattice Invariants

Dimension:$3$
Determinant:$542$
Level:$1084$
Density:$0.179923945493185299415515706242\dots$
Group order:$2$
Hermite number:$0.490599267926125625025450419289\dots$
Minimal vector length:$4$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{4} \) \(\mathstrut +\mathstrut 4 q^{10} \) \(\mathstrut +\mathstrut 4 q^{16} \) \(\mathstrut +\mathstrut 6 q^{18} \) \(\mathstrut +\mathstrut 2 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 10 & 3 \\ 1 & 3 & 16 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$17$
 
$\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 10 & 3 \\ 1 & 3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & -1 \\ 0 & -1 & 136 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 8 & 2 \\ 0 & 2 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 4 & -1 \\ 1 & -1 & 78 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & -1 \\ 2 & 8 & 3 \\ -1 & 3 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & -1 & 68 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & 1 \\ -3 & 8 & 0 \\ 1 & 0 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 10 & 1 \\ 0 & 1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -1 \\ 1 & 10 & 4 \\ -1 & 4 & 16 \end{array}\right)$ ...
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Comments

This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.